674
RAPID POPULATION GROWTH-II
Males
Females
5-9 10-14 15-19 20-24 25-29
The number of men 20 to 24 is far smaller than the number of women 15 to 19, reflecting a very short-lived baby boom in the 1940's.
This boom in Japan was followed by a dramatic decline in births, and the reverse marriage squeeze appears between men of 15 to 19 and women 10 to 14. As these men and women reach marrying age over the next few years the present excess of women will give place to a shortage. Data for later years should tell us to what extent the decline in fertility of the late 1960's (the crude birth rate fell from 18.6 in 1965 to 13.8 in 1966) is due to the disproportion in the numbers of men and women of corresponding marrying ages. The point will be important for other countries in the wake of successful efforts to control fertility. More research is needed; we have neither adequate data nor adequate theory on the response of marriage and childbear-ing to disproportionate numbers of the two sexes. This is a major unsolved problem of theoretical demography.
APPENDIX 1
To trace changes in age-specific birth and death rates to their consequences for overall rates and for age distribution is the main interest of this paper. Its argument depends on a procedure of partial differentiation in the one-sex stable model. The results for birth changes are given in Table A, Appendix 1, which is readable without reference to its derivation.
As an instance of how the table is to be read, if the birth rate mx increases by the quantity Arax, the effect of this on r, the intrinsic rate of natural increase, is an increase of Ar = e~rxpxAmx/K., where px is the probability of living to age x for a child just born, and K. is the mean age of childbearing in the stable population. Further down, the fractional effect of the change in the birth rate at age x on the proportion ca of the population at age a is given as this same value of Ar multiplied by A -a, where A is the mean age in the stable population.
Some of the results of the table go back to Lotka (12), some to Coale (13).n will be more serious than 5 years earlier or 5 years later. (Allowance for military personnel stationed outside the United States—omitted from the above official estimates—would somewhat reduce the effect under discussion.)